Neither of the two verses in the question have Jesus (or anybody else) using the phrase, "the end of the world". People today have all sorts of ideas about what Christians should believe about the world ending (either literally or symbolically), but if we can just stick to what Jesus actually said, the answer might become clear.
First, the Matthew 16:28 statement. Jesus promised that some of his disciples would not die before they saw him "coming in his Kingdom". The very next verse tells us that six days later, he took three of them up a mountain where they saw him transfigured into such glory as they had never seen before. They witnessed Moses and Elijah talking with this glorified Christ. Then God spoke from a bright, overshadowing cloud, saying, "This is my beloved Son, in whom I am well pleased; hear ye him." Then the vision vanished and only Jesus was there with them.
Surely that was the fulfillment of Jesus' promise six days earlier? And also consider 95 A.D. when the aged apostle John had visions of the resurrected glorified Christ in heaven. The descriptions of Christ are of this majestic King of heaven who shares the Father's throne (Revelation 5:5-14 & 19:11-16 & 20:11-13 & 22:1-3). He is crowned, he rules, he judges all the dead whom he has raised, all the powers of evil are defeated by him, and a new heaven and a new earth comes into being. If that was not John seeing Christ coming in his Kingdom power and glory, what was?
Second, the Mark 13:30 statement about the generation that would "not pass" until "all these things be done" (A.V.). What things? From verse 1 till verse 23 Jesus was answering the disciples' question as to when the great Jerusalem temple buildings would be ruined. He built up a prophetic picture of increasingly awful tribulation for his followers (always addressed by him in this chapter as "you"). But he warned them not to heed false Christs claiming they where Christ returned. He warned them that false prophets would arise to try to deceive them. That takes us to the end of verse 22. Now comes a clear division, or section in Jesus' prophecy:
"But take ye heed: behold I have foretold you all things. But in those
days after that tribulation, the sun shall be darkened, and the moon
shall not give her light, and the stars of heaven shall fall, and the
powers that are in heaven shall be shaken. And then they shall see the
Son of man coming in the clouds with great power and glory. And then
he shall send his angels, and shall gather together his elect from the
four winds, from the uttermost part of the earth to the uttermost part
of heaven." Mark 13:23-27 A.V.
Notice how Jesus begins to speak of "they", as opposed to his followers, who he always calls "you"? That's because his followers are all safely and suddenly gathered to him at that time, which is the time "after that tribulation" - the one his followers have gone through. Before they see Jesus in glory, in his Kingdom power descending from heaven to take them safely away, they have gone through great tribulation. Now, has that gathering of the elect to be with Jesus at his return happened yet? No. Are Christians today still going through increasingly great tribulation? Yes. Are Christians in this generation still eagerly awaiting Christ's sudden return as they were in the first century? Yes. So, the answer to the question is that every generation of Christ's followers have longingly awaited seeing him return to Earth in his Kingdom glory, from when Jesus told them to look out for his return, until he actually does return - which has not yet happened.
Yet it is clearly true that those first century Christians did experience great tribulation leading up to the literal fulfilment of the earthly destruction of the Jerusalem temple in A.D. 70. They witnessed that destructions, being protected from it by heeding Jesus' warning to flee once they saw armies encamped around Jerusalem. When those Roman armies suddenly stopped their siege and went away, that was when they fled. When the armies later returned, all who had not heeded Jesus' warning either died horribly or were taken off as slaves. Not the Christians who believed Jesus' prophecy.
The first part of his prophecy having been fulfilled within their generation, the second part then started, which part continues to this day. As explained here:
"The temple would fall amidst dreadful affliction. However this should
pale into insignificance compared to that attending the fall of
Christendom in the coming days of unprecedented tribulation.
Nevertheless the elect are forewarned of the certainty that despite
these signs the end is not yet, not whilst the earth trembles, but
when the heavens change, then the end is nigh. During the former times
tribulation will trouble the whole world, to mount increasingly as the
new - heavenly - portents loom nearer and nearer, Mk. 13:24-27.
Intensifying tribulation on earth; furious persecutions in the world
and from its hostile religion; dreadful global visitations. But the
end is not yet. The elect must endure all with patience, expecting no
relief, knowing that this is but the herald of new signs in a
different and heavenly sphere. 'The sun shall be darkened, and the
moon shall not give her light. And the stars of heaven shall fall, and
the powers that are in heaven shall be shaken.' Then; mark that,
then - not till then - 'Then shall they see the Son of man coming in the clouds with great power and glory.' Mk. 13:26
...The elect being raised from the dead, delivered out of the world,
gathered to Christ in glory, nothing remains for the world, and for
this world's religion, but the fiery deluge, the dissolution of all
things, the resurrection of damnation, the final judgment, and the
vengeance of eternal fire." Mark, John Metcalfe, pp. 183-5, John
Metcalfe Publishing Trust, 1996
Conclusion Summarized: The first century Christians were looking for the destruction of the Jerusalem temple as a major sign indicating Christ's return would happen. But after its destruction in A.D. 70, and Christ still had not appeared by A.D. 95, John had visions of Christ in kingly kingdom power, revealing far more details about events leading up to his sudden return. That fortified the Christians through the next century where, in every succeeding generation they held on to that prophetic word to keep them faithful through increasingly dreadful tribulations - to this very day.
Every generation of Christians has been told enough to keep them looking in faith for Christ's spectacular return to Earth, obediently carrying out God's will for them, and for the honour of his name. Christ told us all that he would go away to a 'far country' [heaven] for a long time, then return to hold everyone to account [the Last Day]. That Day of Resurrection and Judgment is nearly 2,000 years nearer now than it was when Jesus spoke of "that tribulation" (for the early church) and the great tribulation just before his return.